Problem: What is the units digit of the product of all the odd positive integers between 10 and 110?
Any odd multiple of 5 will end in a units digit of 5 (even multiples will end in a units digit of 0). Since all the integers we are multiplying are odd and some of them have a factor of 5, the product will be an odd multiple of 5 with a units digit of $\boxed{5}$.